Jantzen filtration and strong linkage principle for modular Lie superalgebras

2017/10/16 by Lei Pan, Pan, Lei, Bin Shu +1
Mathematics · #17B20 and 17B45 #FOS: Mathematics #Primary 17B50 #Representation Theory (math.RT) #Secondary 17B10 #math.RT #msc:17B10 #msc:17B20 #msc:17B45 #msc:17B50

paper · pdf · doi:10.48550/arxiv.1710.05821

31pages

arxiv created 2017/10/16 · arxiv updated 2017/10/17

Abstract

In this paper, we introduce super Weyl groups, their distinguished elements and properties for basic classical Lie superalgebras. Then we formulate Jantzen filtration for baby Verma modules in graded restricted module categories of basic classical Lie superalgebras over an algebraically closed field of odd characteristic, and prove a sum formula in the corresponding Grothendieck groups. We finally obtain a strong linkage principle in such categories.

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